Was reassured by 2 experienced beekeepers that it can be 3 or 4 weeks before a new queen is mated and starts laying. Sure enough, when I checked the hive on the 15th July, there were at least 4 frames of capped brood. This means she probably started laying about 3 weeks after she emerged.
Have taken advice and put on another brood box, a super and some sugar syrup. The idea is to encourage the bees to draw out all the foundation and to lay down some stores of honey for the winter. Come Spring I can take one of the brood boxes to make a new hive. Having 2 hives makes things easier to manage.
Just downloaded the August edition of the beekeeping magazine, Beecraft. It included a link to this amazing video ‘More Than Honey’ which shows, in high definition video, how a queen is mated.